The extended Eulerian numbers over function fields

Tamagawa Numbers of Algebraic Groups Over Function Fields

Derivatives and Eulerian Numbers

The aim of the present note is to give a closed form formula for the nth derivative of a function which satisfies Riccati’s differential equation with constant coefficients. The paper is organized as follows. In section 2 we recall the definition and basic properties of Eulerian numbers. We introduce and prove the mentioned formula in section 3. Some examples where the formula can be applied ar...

Eulerian-Catalan Numbers

We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.

Equidistribution over function fields

We prove equidistribution of a generic net of small points in a projective variety X over a function field K. For an algebraic dynamical system over K, we generalize this equidistribution theorem to a small generic net of subvarieties. For number fields, these results were proved by Yuan and we transfer here his methods to function fields. If X is a closed subvariety of an abelian variety, then...

Congruences on Stirling Numbers and Eulerian Numbers

In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.